Mathematical Modelling of Electrode Geometries in Electrostatic Fog Harvesters

Abstract: This paper presents a comparative mathematical analysis of electrode configurations used in active fog water harvesting systems based on electrostatic ionization. The study begins with a brief overview of fog formation, typology, and the global relevance of fog as a decentralized water resource. It also outlines the main methods and collector designs currently employed for fog water capture, both passive and active. The core of the work involves solving the Laplace equation for various electrode geometries to compute electrostatic field distributions and analyze field line density patterns as a proxy for potential water collection efficiency. The evaluated configurations include centered rod–cylinder, symmetric parallel multi-rod, and asymmetric wire–plate layouts, with emphasis on identifying spatial regions of high field line convergence. These regions are interpreted as likely trajectories of charged droplets under Coulombic force influence. The modelling approach enables preliminary assessment of design efficiency without relying on time-consuming droplet-level simulations. The results serve as a theoretical foundation prior to the construction of electrode layouts in the portable HygroCatch experimental harvester and provide insight into how field structure correlates with fog water harvesting performance.